The present invention relates to a press for hydrostatic extrusion of tubes. The press contains a pressure chamber which is composed of a high pressure cylinder, a pressure-generating punch insertable into one end of the cylinder and a die inserted into the other end of the cylinder. In the pressure chamber there is arranged a mandrel which is held axially fixed in relation to the die by support members. The tip of the mandrel projects into an opening in the die so that an annular gap is formed, in which a tubular billet is shaped into a tube with dimensions determined by the dimensions of the gap when the billet is subjected to a high all-sided hydrostatic pressure in a surrounding pressure medium. A press of this kind and its mode of operation is disclosed in greater detail in U.S. Pat. No. 3,751,958.